The general objective of the research to be undertaken is to provide applicable and informative statistical methods for the analysis of experiments and the evaluation of therapeutic and other trials in the Biomedical area. The principal focus will be on predictive or observabilistic inference and decision making. This will entail obtaining algorithms for calculating the probability distribution of particular functions of future observables useful in sampling curtailment developing methods for assessing whether certain standard statistical models are robust to particular perturbations, testing for discordancy of possibly aberrant observations, providing optimal rules for administering diagnostic screening programs for a condition or diseast, devising optimal statistical methods for the regulation or control of responses associated with a disease, and comparing the effect on prediction of the estimation of hyperparameters in hierarchical models by maximum likelihood, method of moments and sample reuse techniques.